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math.PR2023★ 3 cited
Multiplicative SHE limit of random walks in space-time random environments
Sayan Das, Hindy Drillick, Shalin Parekh
We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random w…
math.PR2023★ 10 cited
KPZ equation limit of sticky Brownian motion
Sayan Das, Hindy Drillick, Shalin Parekh
We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that…